Dimension subgroups, nilpotency indices, and the number of generators of ideals in p-group algebras

DOI10.1016/0021-8693(90)90228-GzbMath0695.16007MaRDI QIDQ909756

Aner Shalev

Publication date: 1990

Published in: Journal of Algebra (Search for Journal in Brave)

zbMATH Keywords

group algebrametacyclic groupsminimal numbers of generatorsfinite p-groupaugmentation idealLoewy seriescyclic subgroupindex of nilpotencedimension subgroupscyclic subgroup of finite indexresidually-p group

Mathematics Subject Classification ID

Group rings (16S34) Nil and nilpotent radicals, sets, ideals, associative rings (16N40) Group rings of finite groups and their modules (group-theoretic aspects) (20C05) Finite nilpotent groups, (p)-groups (20D15) Modules, bimodules and ideals in associative algebras (16Dxx)

Related Items

THE p-ZASSENHAUS FILTRATION OF A FREE PROFINITE GROUP AND SHUFFLE RELATIONS ⋮ On the upper exponent of a finite \(p\)-group. ⋮ GENERATING IDEALS IN COMMUTATIVE ARTINIAN GROUP RINGS AND A GENERALIZE D PASCAL'S TRIANGLE ⋮ The number of generators of ideals in graded group algebras and \(p\)-adic analytic pro-\(p\) groups of dimension one ⋮ Group rings with n-generated ideals ⋮ NILPOTENCY INDICES OF THE RADICALS OF FINITE p-SOLVABLE GROUP ALGEBRAS. II ⋮ Nilpotency indices of the radicals of p-group algebras ⋮ Group rings R[G with 3-generated ideals when R is artinian] ⋮ The modular group algebra problem for metacyclic 𝑝-groups ⋮ Numbers of generators of ideals in zero-dimensional group rings ⋮ Residually Lie nilpotent group rings ⋮ The derived length of Lie soluble group rings. I ⋮ Nilpotency indices of the radicals of finite p-solvable group algebras, I ⋮ Augmentation-filtration and normal distribution. ⋮ Applications of dimension subgroups to the power structure of \(p\)-groups ⋮ The dilworth number of group rings over an artin local ring ⋮ The nilpotency class of the unit group of a modular group algebra. III

Cites Work

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• Powerful \(p\)-groups. I: Finite groups.
• On the number of generators of ideals in local rings
• A remark on the Loewy-layers of the modular group algebra of a finite p- group
• On the nilpotency indices of the radicals of group algebras of \(p\)-groups which have cyclic subgroups of index \(p\).
• On the Number of Generators and the Modular Group-Ring of a Finite p-Group
• Lie Dimension Subgroups, Lie Nilpotency Indices, and the Exponent of the Group of Normalized Units
• Lie dimension subgroups
• The Structure of the Group Ring of a p-Group Over a Modular Field
• Sur les groupes nilpotents et les anneaux de Lie

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